## Math 120A (Fall 2022)

### Summary

Math 120A is an introduction to complex analysis. We will cover everything from the basic properties of the complex numbers, through to the Residue Theorem on line integrals. See below for a full list of topics.

Unlike the 140ABC and 142AB real analysis courses, we will be more concerned with all the surprising and useful things that are true about complex-valued functions, and what we can do with them, than with supplying complete rigorous proofs of everything. In particular this class is designed to be approachable to someone who has not taken one of the upper-division real analysis sequences (though we will need some basic real analysis). Equally, the course is meant to hold interest for those who have taken these classes, because complex analysis has a different flavor.

There is no required textbook for this course.
However, *Complex Analysis* by T. Gamelin is available online through UCSD and is a recommended optional textbook.

### Contacts

The instructor is Freddie Manners (email `fmanners`); my office is AP&M 7343.
The TA is Bochao Kong (email `bokong`).

### Class and office hours

Lectures are held on Mondays, Wednesdays and Fridays, 1500–1550 (i.e., 3:00pm–3:50pm). Lectures will be held in-person in MOSAIC 0204. They will be podcasted, but in-person attendance is strongly encouraged.

Section will take place in-person at the advertized times and places.

The Google calendar below has times and locations for all class events.

### Exams

There will be two in-class midterms, on **Monday October 17** (Week 4) and **Monday November 7** (Week 7).

The final exam is on **Friday December 9**, at 1500–1800.
It is also in-person (location TBD).

You should ensure at the start of the quarter that you can attend these exams.
In general, alternative modalities, dates or times (in particular, remote exams) will *not* be offered.

### Homework

Homework will be set every week, **due by 2359 each Monday night**. The first homework deadline is on Monday April 4; the last on Monday May 30. There will be some optional homework in week 10 as exam practice.

Midterm weeks will have reduced homework loads and altered deadlines, but still some homework.

Please note: while discussing homework problems in groups is permitted (and encouraged), your final written-up solutions **must be written by you, by yourself, in your own words**. If your homework appears to have been copied directly from another student (or another source) that may constitute an academic integrity issue. You also may **not** post homework questions or solicit answers on the internet.

### Grading

Your **combined grade** for the course is calculated as follows.
First, your lowest homework score is dropped. Then, take 30% homework + 30% midterms + 40% final.

The letter grade cut-offs will be at least as generous as the following table (but may be more generous). Separately, exam scores may be curved to adjust for difficulty.

A+ | A | A- | B+ | B | B- | C+ | C | C- | F |
---|---|---|---|---|---|---|---|---|---|

97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | < 70 |

### Resources

In addition to this website, the course has a Canvas page, a Gradescope page and a Piazza site. The sign-up codes for Gradescope and Piazza are listed on the Canvas home page.

### Provisional schedule

A rough schedule of topics is given below. Note it is very much subject to change and offered as a guideline only.

Week | Mon | Wed | Fri | Topic |
---|---|---|---|---|

0 | L1 | Introduction | ||

1 | L2 | L3 | L4 | The complex numbers and basic properties. The complex exponential and related functions. |

2 | L5 | L6 | L7 | A crash course in topology. The Riemann sphere, stereographic projection. Roots and logarithms. |

3 | L8 | L9 | Review |
Review of real analysis. Power series. |

4 | MT1 |
L10 | L11 | Differentiability. The Cauchy--Riemann equations. |

5 | L12 | L13 | L14 | Conformal maps. Line integrals. Cauchy's Theorem. |

6 | L15 | L16 | Review |
Cauchy's Integral formula. Louisville's Theorem. |

7 | MT2 |
L17 | X | Power series and differentiability at infinity. |

8 | L18 | L19 | L20 | Zeros of holomorphic functions. Laurent series. |

9 | L21 | X | X | The Residue Theorem. |

10 | L22 | L23 | Review |
Further topics and examples (if time). |

### Office hours

Regular office hours and locations are listed in the table below. However, please **check the calendar below** for any one-off changes or cancellations.

Instructor / TA | Location | Regular hours |
---|---|---|

Freddie Manners | AP&M 7343 | Mondays 10:30am – 11:30am, Fridays 4:30pm – 5:30pm |

Bochao Kong | HSS 4025 / Zoom | Monday 4:30pm – 6:00pm / Friday 5:30pm – 7:00pm |

### Course calendar

A link to add this calendar is available on the course's Canvas page.